For a first initial step, I would install and run spybot as well as a good antivirus (not only your own installed antivirus but a good online scanner also like trend micro house call). Its not mandatory but well advised. Second, update firefox. I have had it lockup plenty of times myself (there are some very buggy versions out there). While I prefer firefox, I have opera installed as a backup (some sites just don't like firefox). Further, if you tend to leave the the browser open and develop a lot of tabs like I do, se if any sit there and continiously try to load (weather its frozen up or not). A couple of those will lock up firefox.
While there are hardware problems that could cause it (bad memory), It's more likly a software problem (so not a bad computer). First you need to find out if firefox is locking up or something else is locking it up. In xp hit ctrl, alt and del and it will bring up task manager (in vista which it probably has, hit ctrl, alt and del which should bring up a menu where you can start task manager). Minimise task manager but do not close it. In xp (not sure about vista but I would imagine it would have something similar), there will be a little green box in the task bar that is basically a cpu usage meter. Is it pegged (all light green instead of a green black grid)? Maximise task manager. The first tab shows major programs runniing and will show which are not responding. Are there others that are not responding? If so, either could be at fault. The performance tab will show cpu usage (if it is pegged at 100%, then you need to find what is locking up the cpu's power). It will also show memory (are you running short on physical memory)?
The processes tab will show you what is tying your cpu up if high cpu usage has anything to do with it. Programs running as well as every background process running shows here. If your cpu is pegged, what process is causing it (using a very high percentage of cpu power)? Is it firefox or something else? If it is something else, google the name of the process to find out what it is.
Basically, you are trying to narrow it down to cpu usage problem, a memory shortage problem, or a hardware problem for now (firefox may be tying up the cpu and freezing it, or another program may be using all the cpu power casuing firefox to freeze up). If cpu usage is high, investigate the problematic program or process (you can google processes to find what they are and if it is safe to kill them to see if the problem goes away, then go from there).
In the performace tab, if physical memory is low, you might not have enough memory for everything running on your computer. IF neither seems to be the problem, then mabe look at hardware as a next step.
google and download memtest86. Create a bootable cd, dvd, floppy or flash drive. Most computers default to booting from a cd/dvd or floppy if present but you would probably have to set it to boot from a flash drive. Boot from memtest and let it run (for hours or even all night). If it throws errors, its bad memory (easilly replaceable so the whole laptop is not bad, and warranty should cover it). If not, try googling prime 95 and running it in windows (this will stress your cpu). Again, run it for hours. WARNING!!!! The memory test and much more so the cpu test will generate a lot of heat (and kill your battery fast, have it plugged in). DO NOT block the vents and if at all possible, use a notebook cooler or even aim a desktop fan or something at it to help keep it cool. In therory, the notebook should have proper cooling (running these tests is no diffrent than running a program that takes long, intensive processing), but in reality some notebooks are like ovens and heat kills parts. Thats why every store on the planet that caries a few electronics carries laptop coolers.
Hopefully that will at least get you pointed in the right direction.